#14515029

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, socle	C₂²	C₂²⋊S₅
commutator, cosocle	C₄×SL(2,𝔽₅)	C₂²
Frattini	C₂×C₄	C₂×S₅
Fitting, hypercenter	C₂×D₄	S₅
prime radical	D₄×SL(2,𝔽₅)	C₂
hypocenter	SL(2,𝔽₅)	SD₁₆
LCS	G ▷ C₄×SL(2,𝔽₅) ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₄

194 conjugacy classes of subgroups; only the 18 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 18 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 192

Permutation generators:

(1,34)(2,33)(3,36)(4,35)(5,38)(6,37)(7,40)(8,39)(9,53,32,42,22,63)(10,54,31,41,21,64)(11,55,29,44,24,62)(12,56,30,43,23,61)(13,60,18,46,27,49)(14,59,17,45,28,50)(15,57,20,48,26,51)(16,58,19,47,25,52);(1,8,3,5,2,7,4,6)(13,30,17,23)(14,29,18,24)(15,32,19,22)(16,31,20,21)(25,27,26,28)(33,37,36,40,34,38,35,39)(41,43,42,44)(45,64,50,53)(46,63,49,54)(47,61,52,55)(48,62,51,56)(57,58)(59,60)

Conjugacy classes & character table

45 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240727);